integral from 0 to 2 of x/((1+x^2)^4)

Lösung

\int_{0}^{2} \frac{x}{( 1 + x ^{2} ) ^{4}} d x

\frac{62}{375}

Dezimale

0.16533 \dots

Schritte zur Lösung

\int_{0}^{2} \frac{x}{( 1 + x ^{2} ) ^{4}} d x

Wende U-Substitution an

= \int_{1}^{5} \frac{1}{2 u ^{4}} d u

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int_{1}^{5} \frac{1}{u ^{4}} d u

Wende die Potenzregel an

= \frac{1}{2} [- \frac{1}{3 u ^{3}}]_{1}^{5}

Berechne die Grenzen:

\frac{124}{375}

= \frac{1}{2} \cdot \frac{124}{375}

Vereinfache

= \frac{62}{375}

\int_{0.5}^{1} x d x

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